9/16 - Difference Quotient

This is the difference quotient. An example of how to use the equation is as follows:

f(x) = 2x - 1

Plug it into the difference quotient:

And solve simplify:

 

 

Other notes:

REMEMBER: the Domain is the set of possible inputs. The Range is the set of possible outputs.

Consider the equation  function f(x)=2x-5

• The Domain on this equation function is (-∞,∞), because you can plug any number into the equation to yield a useable result that makes sense with the graph.

Now consider the equation function

• The domain for this equation function is (-∞,3)U(3,∞). The graph cannot touch three, because the denominator cannot equal zero.

Lastly, lets look at the equation function

• This equation function has a domain of [5,∞). the input has to be greater than or equal to five because you cannot take the square root of a negative number.